The paper reviews the works devoted to convex spiral autowaves, which are widely known. Recently a new type of autowaves has been discovered - concave autowaves,
they propagate from the periphery of active media to the center and are capable of transfering energy. It is proved that concave spiral autowaves can exist in specific
inhomogeneous active media. Their existence is confirmed by computational experiments. It is established that concave autowaves are widespread in nature. The article gives
a more detailed review of the biological and medical applications of spiral concave autowaves, it is also known that there are many of them in physics, chemistry, hydrodynamics,
meteorology, and space. Concave spiral autowaves, carrying energy, are one of the essential tools of self-organization.
Purpose of the study. The aim of the study is to improve the methodological apparatus of cognitive modeling of socio-economic systems (SES) and predicting the indicators of their functioning and development, which ensures an increase in the accuracy and reliability of the results obtained. Existing models and methods do not fully provide the necessary accuracy and reliability of models that requires the development of the mathematical apparatus of cognitive modeling in terms of improving the quality of the developed cognitive models.Materials and methods. To achieve this goal, methods of an integrated approach to solving the problem, decomposing it into interrelated stages, describing the content of each stage in their relationship and presenting a generalized version of the methodology, taking into account the characteristics of the object of study, were used. The developed approach provides creating a more accurate and reliable cognitive model. The effectiveness of the developed methodological apparatus is shown.Results. A detailed analysis of the existing criteria and approaches to solving the problem of verification of cognitive models was carried out, which showed the absence of a unified methodology and an integrated approach in solving problems of cognitive modeling of SES based on cognitive maps. A set of techniques that implement the stages of cognitive modeling has been developed. The results of a comparative analysis of the developed approach with the existing ones are presented.Conclusion. A comprehensive solution to the problem of creating a cognitive model for analyzing and predicting the activities of a university is proposed, which includes a set of stages: the stage of creating the problem field of the situation; identification of factors and relationships between them; the stage of making a cognitive map and its verification, as well as the stage of analyzing the system characteristics of the cognitive model, validating the cognitive model. The developed methodological apparatus includes a set of techniques aimed at obtaining an adequate model that provides more accurate and reliable results of modeling the object of study.
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